The sum of the squares of two consecutive even natural numbers is loo. Find the numbers.​

Question

The sum of the squares of two consecutive even natural
numbers is loo. Find the numbers.​

in progress 0
Maria 1 month 2021-08-17T14:51:20+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-17T14:52:54+00:00

    Answer:

    Step-by-step explanation:

    Let x and (x+2) be the two consecutive even natural number.

    therefore

    According to the given condition

    x2 + (x + 2)2 = 100

    ∴  x2 + x2 + 4x + 4 = 100

    ∴ 2×2 + 4x + 4 – 100 = 0

    ∴  2×2 + 4x – 96 = 0

    Dividing by 2 we get,

    x2 + 2x – 48 = 0

    ∴  x2 – 6x + 8x – 48 = 0

    ∴  x (x – 6) + 8 (x – 6) = 0

    ∴  (x – 6) (x + 8) = 0

    ∴  x – 6 = 0 or x + 8 = 0

    ∴  x = 6 or x = – 8

    x is an natural number

    ∴  x cannot be  – 8

    ∴  x = 6

    And x + 2 = 6 + 2 = 8

    ∴  The two consecutive even natural numbers are 6 and 8 respectively.

    0
    2021-08-17T14:53:17+00:00

    Answer:

    The two consecutive even natural numbers are 6 and 8

    Step-by-step explanation:

    Let the two consecutive even natural numbers be x and x+2

    x^{2} +(x+2)^2=100\\x^2+x^2+4x+4=100\\x^2+x^2+4x+4-100=0\\ 2x^2+4x-96=0\\

    When we divide it by 2 we get,

    x^2+2x-48=0\\x^2-6x+8x-48=0\\x(x-6)+8(x-6)=0\\(x+8)(x-6)=0\\

    ∴x-6=0 or x+8=0

    ∴x=6 or x=-8

    x is a natural number so it cannot be -8

    ∴x=6

    ∴x+2=6+2=8

    ∴The two consecutive even natural numbers are 6 and 8

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )